Finite Group DatabasebetaFinite Group Databasebeta| order | 1872 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | SL(2,𝔽3)×D39 |
| unambiguous semidirect product | C3⋊(SL(2,𝔽3)×D13) |
| Fitting, derived | C3×Q8×C13 ⋊ C2×C3 |
| Sylow | C13 ⋊ D3×SL(2,𝔽3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | A4×D39 |
| commutator, Fitting, cosocle, hypocenter | C3×Q8×C13 | C2×C3 |
| socle | C2×C3×C13 | C2×A4 |
| LCS | G ▷ C3×Q8×C13 | |
| UCS | C1 ◁ C2 | |
78 conjugacy classes of subgroups.
| transitive degree | μt(G) = 312 |
147 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1872, 774);